Magnetization quantum tunneling and improper rotational symmetry

Abstract

We examine the magnetization quantum tunneling (MQT) behavior expected for a single-molecule magnet (SMM) with improper rotational symmetry. The simplest possible realization is the [NiII(hmp)(dmb)Cl]4 cubane complex that crystallizes in the I41/a space group, resulting in S4 molecular point-group symmetry. A mapping is performed of the energy-level diagram obtained via exact diagonalization of a multi-spin Hamiltonian onto that of a giant-spin model which assumes ferromagnetic coupling and a spin S=4 ground state. The results are compared with a similar analysis for a C3 symmetric Mn3 SMM (S=6 ground state). In the even rotational case (Ni4), the time-reversal invariance associated with the spin–orbit interaction gives rise to a zero-field spin-Hamiltonian that possesses an additional mirror plane perpendicular to the S4 axis, which is not a symmetry element of the molecular point-group. This conclusion applies quite generally to any molecule with improper rotational symmetry (Sq, with q even), including the more widely studied Mn12 SMM. The combined Ni4 and Mn3 studies lead to some interesting predictions concerning MQT selection rules in molecules with even versus odd rotational symmetries. We conclude by considering a case with essentially no symmetry at all, by deliberately distorting the high-symmetry Ni4 molecule. In this case, finite gaps are found at all intersections in the energy-level diagram, indicating a complete absence of MQT selection rules.